Simple vibration modeling of structural fuzzy with continuous boundary by including two-dimensional spatial memory.

Many complicated systems of practical interest consist basically of a well-defined outer shell-like master structure and a complicated internal structure with uncertain dynamic properties. Using the "fuzzy structure theory" for predicting audible frequency vibration, the internal structure is considered as one or more fuzzy substructures that are known in some statistical sense only. Experiments have shown that such fuzzy substructures often introduce a damping in the master which is much higher than the structural losses account for. A special method for modeling fuzzy substructures with a one-dimensional continuous boundary was examined in a companion paper [L. Friis and M. Ohlrich, "Vibration modeling of structural fuzzy with continuous boundary," J. Acoust. Soc. Am. 123, 718-728 (2008)]. In the present paper, this method is extended, such that it allows modeling of fuzzy substructures with a two-dimensional continuous boundary. Additionally, a simple method for determining the so-called equivalent coupling factor is presented. The validity of this method is demonstrated by numerical simulations of the vibration response of a master plate structure with fuzzy attachments. It is revealed that the method performs very well above a nondimensional frequency of 500 of the master, and it is shown that errors below this frequency are caused mainly by simplifying assumptions concerning the shape of the master vibration displacement.